These constraints are local and define an extension \(\mathcal {E}_{h}^{\mathrm {ag}}: V_{h}^{\mathrm {in}} \rightarrow V_{h}^{\mathrm {ag}}\) . In fact, the aggregated finite element space is the image of this extension operator. The method satisfies the desired approximation properties and the extended \(L^2(\Omega _h)\)  and \(H^1(\Omega _h)\)  stability in (REF ) and (REF ); see [1]} for more details. We also refer to [2]} for an alternative definition of the discrete extension operator that relies on interpolation for high-order polynomial bases and to [3]}, [4]}, [5]} for the extension of higher-order continuous (isogeometric or spline-based) discretizations. The definition of a space-time discrete extension operator for moving domains and interfaces can be found in [6]}.
